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Exploring lines II

Background

Three lines can make many closed and open figures. In fact the minimum number of lines required to make a closed figure is three. A closed figure is one that encloses a space within it completely. Otherwise the figure is open. A closed figure made out of three line segments has three sides and is called a triangle.

Aim

Arrange three lines in different ways to make both closed and open figures.

Activities

Arrange three sticks so that all of them are parallel to each other. How will you ensure that they are parallel to each other? Do they form a closed or an open figure?

Arrange the same three sticks to form different open figures. How many could you make?

Arrange the three sticks so that they are all collinear. In how many different ways can you make this arrangement?

Arrange the three sticks such that they form a closed figure. How many sides does the closed figure have?

In how many different ways can you arrange the sticks to make different looking closed figures of three sides (it is not necessary for the ends of the stick to meet)?

Related Questions

If you arrange three sticks of equal length, such that their ends meet, how many triangles can you make?

If you arrange the same sticks and make them intersect each other, not at the end points but anywhere on the sticks, how many different triangles can you make?

Choose a long stick. Break it into three parts. Can you arrange them to form a triangle? Ensure that the ends meet.

If your answer to the above question is yes, then break the shortest stick in to three parts. Use two of these sticks and the longest unbroken stick to form a triangle. Could you do it? Why?

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